The views expressed in this paper are those of the author and do not necessarily represent those of the

BNA Working Paper BNA.WP/06/2

PPP Theory in a Fixed Exchange Rate System

Miriela G. L. Carolina

The views expressed in this paper are those of the author and do not necessarily represent those of the

Bank van de Nederlandse Antillen.

August 18, 2006

Abstract

In a …xed exchange rate system, the PPP theory implies equality be- tween in‡ation rates of the anchor country and the …xed exchange rate country. However, in‡ation rate di¤erentials do exist in a …xed exchange rate system. In this paper, I show that by assuming a linear relationship, there is weak evidence for the PPP to hold and that the in‡ation rate di¤erentials are consistent with the PPP theory.

JEL Classi…cation: C32, E31, F31.

Keywords: PPP theory, …xed exchange rate system, …xed-to-the dollar exchange rate system.

1 Introduction

This working paper deals with the implications of the validity of the Purchas- ing Power Parity (PPP) theory in the …xed-to-the dollar environment of the Netherlands Antilles. The focus will be on the bilateral exchange rate relation- ship between the United States and the Netherlands Antilles’¹ economy. In this paper, I assume the process to be linear and describe it by using an error- correction model. According to the relative PPP theory, exchange rate changes are determined by domestic and foreign in‡ation. In a …xed exchange rate en- vironment,² the PPP theory collapses into an ‘in‡ation rate equality’theory. If

1The …ve Caribbean Islands of the Netherlands Antilles (N.A.), although part of the Dutch Kingdom, have their own currency, which is pegged to the U.S. dollar. The majority of goods is imported, and the main export is services. Imports are mainly from the United States, the Caribbean, and Europe.

2Economies with currencies pegged to the U.S. $ are e.g., Aruba, the Bahamas, Barbados, Belize, and the Netherlands Antilles. Seventy countries have exchange rate arrangements with one exchange rate anchor (source: International Financial Statistics, yearbook 2002).

PPP holds in this case, in‡ation rates between the anchor country and the …xed exchange rate economy are equal. Empirical results show that in‡ation rate dif- ferentials exist in a …xed exchange rate system. Are these di¤erentials the short run deviation from the PPP? The literature provides abundant evidence and plausible answers for the deviation of the PPP theory: tari¤s, transportation costs, nontari¤ barriers, in‡ation di¤erentials in traded and non traded goods (the Harrod Balassa Samuelson e¤ect) are just a few theories. Developments in cointegration analysis contributed to the revival of interest in the PPP the- ory in the 1990s. Still, researchers are not unequivocal on the PPP hypothesis.

A study by MacDonald (1995) suggested a long run relationship between the exchange rate and prices in the developed countries. More recent studies by Rambarran (1998), and Darius and Williams (2000) showed weak evidence of a long run relationship for some Caribbean countries. In studies of cointegration, the null hypothesis of no cointegration is more often rejected in a …xed exchange rate regime when compared to a ‡oating system. In general, researchers have come to the conclusion that rejection of the PPP theory is due largely to lack of power of the tests ( Sarno and Taylor (2002)).

Furthermore, based on recent studies by Sarno (2003), the process of devia- tions from PPP is believed to be a nonlinear process, rather than the presumed linear approach. The nonlinear approach is beyond the scope of this paper. The paper is divided into the following sections. Section 2 treats the general theory of the PPP and presents a model adapted for a …xed-to-the dollar environment.

Section 3 presents the data. The empirical results are presented in section 4, and concluding remarks in section 5.

2 Theory of the PPP and a Linear PPP Model in a Fixed Exchange Rate System

2.1 Theoretical Speci…cation

The theory of the PPP explains the bilateral relationships between countries in the trading of goods. Basically, the PPP theory is founded on three assump- tions: (1) the Law of one Price (LOP) (2) related to the …rst assumption, the arbitrage mechanism, and (3) a constant real exchange. The best-known exam- ple applied to the …rst assumption is the worldwide price comparison of the Big Mac hamburger. Applying the LOP to this case clearly shows that the LOP is invalid, because Big Mac hamburgers are di¤erent in each country. The second assumption requires, continuously well informed markets, which is not always the case. The third assumption, a constant real exchange rate, is a fundamental assumption for the PPP to hold.

The absolute PPP theory assumes the LOP. For an identical item in both countries, the following relationship holds:

P_tⁱ = St P_t^;i (1) Where:

P_tⁱ : The domestic price of good i, P_t^;i : The foreign price of good i, and

S_t : The (nominal) exchange rate of the domestic currency in a unit of foreign currency.

By summing all prices of tradable goods, the absolute PPP equation is ob- tained:

St= Pt

P (2)

Where:

Pt : the weighted average domestic price of all goods, P : the weighted average foreign price of all goods.

Equation 2 can be rede…ned as follows:

S_t P_t

P_t = 1 (3)

The left-hand side of equation 3 is the real exchange rate, E. Testing the validity of the PPP theory is the same as testing for the real exchange rate to be equal to one. In other words, one unit of good i in the domestic country is equal to one unit of good i in the foreign country. Since trade barriers, transportation cost, preferences, and other factors will impede equation 2 from holding, it is assumed that these factors can be accumulated in a constant factor

. In other words, the real exchange rate is constant.

St

P_t

P_t = E = (4)

In logs

st= + pt p_t (5)

Taking the …rst di¤erences of equation 5, the relative PPP is obtained:

st= pt p_t (6)

The interpretation of equation 6 is that the change in the exchange rate (depreciation/appreciation) is equal to the di¤erence in the changes in prices in the two countries. For the PPP to hold, has to be zero. If 6= 0, equation 6 can be considered as the deviation from PPP. Or, if di¤ers from zero in the short run, the real exchange rate deviates from the PPP theory in

the short run. Consequently, an equilibrium error is allowed in the short run when measuring the PPP hypothesis. The PPP theory can be tested in multiple ways. In this paper, I tested the PPP theory using the two most conventional tests. First, I tested whether the real exchange rate/the real e¤ective exchange rate contains a unit root. If it is di¢ cult to reject the unit root behavior of the real exchange rate/the real e¤ective exchange rate, then the real exchange rate/real e¤ective exchange rate follows a random walk and lacks convergence.

The second approach is the test for cointegration between the exchange rate and the relative prices. If the variables are cointegrated, the PPP theory holds.

As stated in equation 6, short run equilibrium errors are acceptable. However, the equilibrium errors must be stationary for the exchange rate and the relative prices to be cointegrated.

2.2 Empirical Speci…cation of the Vector Error Correction Model

I assumed the process of the relative PPP to be linear and applied a vector error correction model based on the cointegration theory proposed by Engle and Granger (1987), the two step procedure. A general speci…cation of a vector error correction model (VECM) of the (n x 1) vector ytis as follows:

yt= ₀+ yt 1+ ₁ yt 1+ ₂ yt 2+ ::: + _q yt q+ "t (7) Where:

0 : an (n x 1)vector of intercept terms,

i : an (n x n) coe¢ cient matrix for all i = 1; :::; q;

: a matrix with elements, with one or more elements nonzero, and

"_t : a (n x 1) vector of white noise disturbances.

To describe the process as equation 7, the data must meet the following criteria: (1) the components of y_t must be of the same order, and (2) the estimated errors of the long run relationship between the components of y_tmust be stationary. If these criteria are met, the variables in the relationship are cointegrated. The long run relationship by the components of yt are estimated using Ordinary Least Squares (OLS). The optimal lag length, q, is derived by

2 tests. In an adequate model, the residuals of the equations are white noise.

The speci…cation in the bilateral case of the Netherlands Antilles-United States relationship is as follows:

pt

f_t = ¹

2 + ^p

f [pt 1 0 1 ft 1] + ^{1;1 1;2}

2;1 2;2

pt 1

f_{t 1} +::: ^{1;1 1;2}

2;1 2;2

p_{t q}

f_{t q} + "_p;t

"_f;t (8)

Where:

pt : the price index of the Netherlands Antilles in logs,

f_t : the foreign price expressed in domestic currency f_t= s_t+ p_t, s_t : the nominal exchange rate in logs, and

p_t : the price index of the U.S. in logs.

The vector yt de…ned in equation 7 is represented in equation 8 by yt = [pt; ft]⁰. The coe¢ cients pand f are called the speed of adjustment parame- ters. It is possible for one of the speed of adjustment parameters to be zero. For example, if ft is not signi…cantly di¤erent from zero, this means that ft does not respond to the discrepancy in the long run disequilibrium, and pt does all the adjustment. In this case, ftis weakly exogenous.

The other components, p_{t q}, and f_{t q} are the short run deviations from the long run equilibrium.

The …rst step is to test whether the components of the vector y_t= [p_t; f_t]⁰ are integrated of the same order. The augmented Dickey-Fuller test is applied to test the order of integration. If both variables of y_t are of the same order, then the long run equilibrium relationship is estimated using OLS. This esti- mated relationship, pt= ₀+ ₁ ft, does not imply the variables of yt to be cointegrated. If the estimated errors of the long run relationship are stationary, the variables are cointegrated.

3 Data

As mentioned, two approaches were used to test the PPP theory. The …rst approach tested the unit root of the real e¤ective exchange rate (REER) and the real exchange rate, (RER), which is de…ned by equation 4. The second approach used the VECM described in the previous section. The data used in the VECM are the consumer price indexes of the United States and the Netherlands Antilles and the nominal exchange rate of the Netherlands Antilles.

The data used in both approaches are monthly indices. The consumer price index (CPI) of Curacao served as a proxy for the CPI of the Netherlands An- tilles. The source was the Central Bureau of Statistics. The sample period was January 1987 to December 2004. The CPI of the United States and the REER of the Netherlands Antilles were both obtained from the International Finan- cial Statistics. The data of the REER were unavailable after July 1999. The nominal exchange rate of the Netherlands Antilles has been pegged to the U.S.

$. since 1971, at f l 1.79 per 1 U.S. $.

3.1 In‡ation Rates

The …rst graph (Figure 1, appendix) represents the month-to-month percentage change in the CPI of the Netherlands Antilles and of the United States. The graph clearly shows that the in‡ation rates in the two countries di¤ered (di¤er- ence in monthly in‡ation rates on the right-hand axis). Moreover, the in‡ation

rate of the Netherlands Antilles showed high volatility in October 1990 and in October 1999. The 1990’s hike, was due to the increasing oil prices resulting from the Gulf war. The spike in October 1999 was attributed mainly to the rise in the turnover tax from 2% to 5%. The one-year in‡ation rates (Figure 2) show that although they di¤ered (di¤erence in the annual in‡ation rate on the right-hand axis), they appear to have a comovement.

3.2 Real Exchange Rates

The REER is a stationary process as the KPSS³ test was not able to reject stationarity, and the ADF⁴ test rejected the unit root hypotheses at conven- tional levels (Table 1). Data for the REER is presented in Figure 4. Graph 3 is the representation of the RER as presented by equation 4. The RER shows a tendency to increase. However, the theory of the PPP does not allow for a deterministic time trend. In the next section, the tests will show that the hypothesis of a trend in the data is rejected. The KPSS test rejected the hy- pothesis of stationarity, and the ADF test gave weak evidence of rejecting the unit root hypothesis (Table 1). In the next section, more comprehensive results are presented.

4 Empirical Results

The …rst method for testing validity of the PPP is a unit root test on the exchange rates, the REER and the RER. The alternative test of the PPP, uses cointegration or the vector error correction described in section 2.2. As already shown, the REER of the Netherlands Antilles (Table 1) is stationary, meaning that the PPP holds. In addition, the RER was tested on stationarity, using the Dickey-Fuller tests (Table 2). To test, the autogenerating process of the RER must be known. In this paper, I focus on three data-generating processes for the RER:

1. In model a, it is assumed that the data-generating (autoregressive) process of the real exchange rate contains a drift term and a trend.

2. In model b, the data-generating process contains a drift.

3. In model c, the data-generating process contains no drift term or a trend.

The model with the lowest AIC and SBC⁵ was selected, which was the model with an autoregressive component of the real exchange rate and the constant term, model b. Furthermore, the AC (autocorrelation) and the PAC (partial au- tocorrelation) indicate the process as AR(1) without a seasonal pattern. Using

3Kwiatkowki-Phillips-Schmidt-Shin test on stationarity.

4Augmented Dickey-Fuller unit root test.

5AIC is the Akaike Information Criterion and SBC is the Schwartz Bayesian Criterion.

the selected model, weak evidence is found of stationarity⁶ in the RER, showing some evidence of the validity of the PPP theory. We can conclude that the REER gives evidence for the PPP to hold, and the RER gives weak evidence for the validity of the PPP in the relationship between the Netherlands Antilles and the United States.

Vector error correction o¤ers an alternative for testing PPP, and it gives the following results. Recall the VECM, equation 8, as described in section 2.2.

The variables, consumer prices of the United States, and of the Netherlands Antilles (Table 3) are both I(1). According to the Engle and Granger procedure, we can estimate the long run equilibrium relationships using OLS. To give a better …t, I tried the following:

The long run equation was estimated by including dummies for October 1990 and 1999. The equation including dummies showed comparable re- sults to the equation without dummies. I excluded the dummies in the equation.

The long run equation was estimated with and without a constant term.

Including the constant is consistent with the relative PPP theory.

Two estimated long run equations (one including a constant and one without a constant) are presented (standard errors in parentheses).

pt= 0:23

(0:03)+ 0:84

(0:006) ft+ et (9)

pt= 0:89

(0:002) ft+ et (10)

I proceeded with the long run equation with a constant, consistent with the relative PPP theory. This theory is more plausible, because it takes into account the transportation cost, preferences, and trade barriers. Stock (1987) proved that if the variables are cointegrated, the OLS estimators in the long run, (equation 9), are superconsistent. Next, I tested for the variables pt; and ft to be cointegrated. The variables are cointegrated of the order (1,1) if the estimated residuals fe^{^}tg of equation 9 are stationary. With the Engle-Granger test, the null hypothesis of a unit root is rejected at 10% signi…cance level (Table 4). The variables are cointegrated and can be described by a VECM.

Two de…nitions of in‡ation rates were taken into account for modeling the error correction:

1. The month-to-month in‡ation rate:

pt= log(cpi_na)t log(cpi_na)t 1 (11) The same for ft:

6The KPSS test rejected stationarity for the real exchange rate. However, the ADF test showed a weak evidence of rejecting the unit root.

ft= log(cpi_usa s)t log(cpi_usa s)t 1 (12) 2. The annual in‡ation rate:

p_t= (1 L₁₂)p_t= ₁₂log(cpi_na)_t (13) same for f_t.

Model (1)

The …rst model, (1), used the month-to-month in‡ation rates.

p_t

ft =

2 4

0:0003

(0:0009)

0:0007

(0:0004)

3 5 +

2 4

0:06

(0:03)

0:0002

(0:01)

3

5 [p_{t 1} 0:23 0:84 f_{t 1}]

+ 2 4

0:03

(0:08)

0:32

(0:2)

0:08

(0:04)

0:4

(0:07)

3

5 pt 1

f_{t 1} + 2 4

0:01

(0:08)

0:18

(0:2)

0:02

(0:04)

0:1

(0:08)

3

5 pt 2

f_{t 2}

+ 2 4 0:07

(0:07) 0:12

(0:2)

0:008

(0:04) 0:05

(0:08)

3

5 p_{t 3} f_{t 3} +

2 4 0:08

(0:07) 0:03

(0:2)

0:008

(0:04) 0:05

(0:08)

3

5 p_{t 4} f_{t 4}

+ 2 4

0:09

(0:07)

(0:16)0:07 0:02

(0:03)

0:08

(0:08)

3

5 p_{t 5} f_{t 5} +

2 4

0:2

(0:07)

(0:16)0:05 0:08

(0:03)

0:08

(0:08)

3

5 p_{t 6} f_{t 6}

+ 2 4 0:08

(0:07) 0:34

(0:16) (0:04)0:01 0:01

(0:08)

3

5 pt 7

ft 7 + 2 4

0:01

(0:07) 0:25

(0:16) (0:03)0:04 0:02

(0:08)

3

5 pt 8

ft 8

+ 2 4

0:06

(0:07)

(0:16)0:10 0:02

(0:03)

0:07

(0:08)

3

5 p_{t 9} f_{t 9} +

2 4

0:05

(0:08) (0:16)0:13 0:02

(0:04)

0:1

(0:08)

3

5 p_{t 10} f_{t 10}

+ 2 4

0:03

(0:07)

0:05

(0:16)

0:02

(0:03) 0:1

(0:08)

3

5 pt 11

ft 11 + 2 4

0:03

(0:07)

0:04

(0:16)

0:1

(0:03) 0:09

(0:08)

3

5 pt 12

ft 12

+ "p;t

"f;t (14)

(1) Standard errors in parentheses

(2) Q statistic on the errors Q(4)=0.06 (1), Q(8)= 0.25 (1), Q(12) = 0.6 (1).

(3) Q statistics on the squared errors: Q(4)=4.1 (0.4), Q(8)=4.5 (0.8), Q(12)=7.9 (0.7)

(4) Q(n) reports the Ljung-Box statistics for autocorrelation of n residuals

in the estimated model. The p value is in parentheses.

The lag length tests indicated a length of four using ² tests on p_t of equation 14. The Ljung-Box Q statistics showed no serial correlation, neither Arch or Garch errors. However, f_tof equation 14 with four lags, showed serial correlation. This equation was expanded up to 12 lags. If the lag lengths of equation f_tare di¤erent from equation p_t, the seemingly unrelated regression error-correction model must be applied. I chose similar lag lengths in both equations. The errors of both equations, fep;t^{^} g; fef;t^{^} g, appear to be white noise.

Model (1) is interpreted as follows: With one unit deviation from the long run PPP in period t 1, the Netherlands Antillean price index falls by 0.06 units and can lead the Unites States price index to fall by 0.0002 units. The speed of adjustment in absolute terms of the Netherlands Antilles is 25 times larger when compared to the United States, indicating the impact of a large economy like the United States on the adjustment process. The speed of adjustment of the Netherlands Antilles is signi…cant ( t value = 2:0), whereas the U.S.

speed of adjustment is not signi…cantly di¤erent from zero ( t value = 0:02), which means that the U.S. prices are weakly exogenous.

Model (2) showed a similar speed of adjustment on the price index of the Netherlands Antilles, but di¤erent speed of adjustment of the U.S price index.

(However, the speed of adjustment of the U.S. price index is insigni…cant). I included the term "t 12due to the seasonality pattern in the data.

p_t

f_t =

2 4 0:06

(0:02)

0:0005

(0:007)

3

5 [p_{t 1} 0:23 0:84 f_{t 1}] 2

4 0:82

(0:08) 0:56

(0:19)

0:02

(0:03) 1:3

(0:08)

3

5 p_{t 1} f_{t 1} +

2 4

0:009

(0:1) 0:12

(0:31)

0:005

(0:04) 0:5

(0:12)

3

5 p_{t 2} f_{t 2}

+ 2 4

0:09(0:1) 0:02

(0:31)

0:04

(0:04) (0:13)0:16

3

5 pt 3

ft 3 + 2 4

0:04

(0:1) 0:4

(0:32) (0:04)0:06 0:09

(0:13)

3

5 pt 4

ft 4

+ 2 4

0:16

(0:1) 0:31

(0:32)

0:08

(0:04)

0:12

(0:13)

3

5 p_{t 5} ft 5 +

2 4

0:04

(0:1)

0:1

(0:31)

0:03

(0:04)

0:04

(0:13)

3

5 p_{t 6} ft 6

+ 2 4 0:2

(0:1) 0:27

(0:32) (0:04)0:09 0:05

(0:13)

3

5 pt 7

ft 7 + 2 4

0:04

(0:1)

0:52

(0:31) (0:04)0:02 0:06

(0:13)

3

5 pt 8

ft 8

+ 2 4

0:1

(0:1) 0:2

(0:31)

0:04

(0:04)

0:02

(0:13)

3

5 pt 9

ft 9 + 2 4

0:02

(0:1) 0:38

(0:32)

0:007

(0:13)

(0:13)0:19 3

5 pt 10

ft 10

+ 2 4

0:02(0:1) 0:27

(0:31)

0:05

(0:03) 0:15

(0:13)

3

5 pt 11

f_{t 11} + 2 4

0:12

(0:08) 0:21

(0:2)

0:04

(0:03)

0:03

(0:08)

3

5 pt 12

f_{t 12}

+h 0:94

(0:02)

0:91

(0:02)

i "p;t 12

"f;t 12 + "p;t

"f;t (15)

(1). Standard errors in parentheses

(2). Q statistic on the errors Q(4)=0.27 (0.96), Q(8)= 0.57 (0.99), Q(12) = 4 (0.96)

(3). Q statistics on the squared errors: Q(4)=3.8 (0.27), Q(8)= 4.18 (0.75), Q(12) = 19(0.06).

The second model used the annual in‡ation rates. This model is interpreted as follows: Again, a one unit deviation from the long run PPP in period t 1 = t 13, which would induce the price index of the Netherlands Antilles to fall by 0.06 units. The t value indicates the speed of adjustment of the United States to be insigni…cant, which means that the U.S. price index is weakly exogenous.

Both VEC models show that short run deviations on the long run equilibrium does exist and that the U.S. price index is weakly exogenous. Both models estimated the speed of adjustment of the Netherlands Antillean price index as -0.06. As shown in the VECM, the di¤erentials in the prices of the United States and the Netherlands Antilles are consistent with the PPP theory. These di¤erentials, i;j pt j ( i;j) ft j; are the short term deviations from the long run path.

5 Concluding Remarks

The main question of this research was centered on the existence of the in‡ation rate di¤erentials in a …xed exchange system when it is assumed that the PPP theory holds. In this paper, I found evidence of the validity of PPP theory in the case of a …xed exchange rate system of the Netherlands Antilles. Empirical tests, using a linear approach, show a cointegrated relationship between the in‡ation rates of the anchor country (United States) and an economy with a …xed exchange rate system (Netherlands Antilles). The VECM shows the existence of short run deviations from the long run trend. As shown, the short term deviations in the VECM are in‡ation rate di¤erentials. This means that in‡ation rate di¤erentials can exist when assuming the PPP theory and can be interpreted as deviations from the PPP in the short run.

Topics for further research include a nonlinear approach and a panel study of countries that are …xed to the dollar, which will provide a broader database.

References

Bahmani-Oskooee, M. (1993): ‘Purchasing Power Parity Based on E¤ective Exchange Rate and Cointegration: 25 LDCs’Experience with its Absolute Formulation,’World Development, Vol. 21, No. 6, 1023-1031.

Boothe, P., Glassman, D. (1987): ‘O¤ the Mark: Lessons for Exchange Rate Modelling,’ Oxford Economic Papers, NS, Vol. 39, No. 3, (Sep., 1987), 443-457.

Darius, R., Williams, O. (2000): ‘An Examination of the Purchasing Power Parity Hypothesis in a Low In‡ation Environment,’Money A¤airs, XIII,1.

Economic Commission for Latin America and the Caribbean (2003): ‘Exchange Rate Regimes in the Caribbean,’LC/CAR/G.715.

Engle, R., F., Granger, C. W. J. (1987): ‘Co-Integration and Error Correction:

Representation, Estimation and Testing,’Econometrica, 55,2,251-276.

Fisher, E., Park, J. (1991): ‘Testing Purchasing Power Parity under the Null Hypothesis of Co-Integration,’ The Economic Journal, Vol. 101, No. 409, (Nov., 1991), 1476-1484.

Frankel, J. (1982): ‘The Mystery of Multiplying Marks: A Modi…cation of the Monetary Model,’The Review of Economics and Statistics, Vol. 64, No. 3, (Aug., 1982), 515 - 519.

Frankel, J. A., Rose, A. K. (1995): ‘A Panel Project on Purchasing Power Parity: Mean Reversion Within and Between Countries’, NBER Working Papers Series, 5006.

Greene, W. H.(2000): ‘Econometrics Analysis,’Prentice Hall, fourth edition.

Leon, H. , Najarian, S. (2003): ‘Time-Varying Thresholds: An Application to Purchasing Power Parity,’IMF Working Paper, 03/181.

MacDonald, R. (1995): ‘Long Run Exchange Rate Modelling,’IMF Sta¤ Papers, 42,3,437-489.

MacDonald, R. (1997): ‘What Determines Real Exchange Rates? The Long and Short of It,’IMF Working Paper, WP/97/21.

Meese, R. A., Rogo¤, K. (1983): ‘Empirical Exchange Rate Models of the Sev- enties: Do They Fit Out of Sample?,’Journal of International Economics 14, 3-24.

Obstfeld, M., Rogo¤, K. (2000): ‘The Six Major Puzzles in International Macro- economics: Is There a Common Cause?,’372-382.

Rambarran, A. (1998): ‘Purchasing Power Parity (PPP) in the Caricom Region, 1973 - 1995, Evidence and Policy Implications,’unpublished.

Sarno, L., Taylor, P. (2002): ‘Purchasing Power Parity and the Real Exchange Rate,’IMF Sta¤ Papers, 49,1,65-105.

Sarno, L., (2003): ‘Nonlinear Exchange Rate Models: A Selective Overview.’

IMF Working paper, 03/111.

Stock, J. (1987): ‘Asymptotic Properties of Least-Squares Estimators of Coin- tegrating Vectors,’Econometrica 55, 1035-56.

APPENDIX

-2 -1 0 1 2 3

4 -4

-3 -2 -1 0 1 2

1988 1990 1992 1994 1996 1998 2000 2002 Difference monthly inflation rate US/NA Inflation rate NA

Inflation rate US

(% ) (% )

Figure 1: Monthly In‡ation Rates

-2 0 2 4

6 -3

-2 -1 0 1 2 3

1988 1990 1992 1994 1996 1998 2000 2002 Annual inflation rate US

Annual inflation rate NA

Difference in inflation rates US/NA

(%) (%)

Figure 2: Annual In‡ation Rates

1.00 1.04 1.08 1.12 1.16 1.20 1.24

1988 1990 1992 1994 1996 1998 2000 2002 Real Exhange Rate

(Jan.1987=1)

Figure 3: Real Exchange Rate

87 88 89 90 91 92 93 94 95 96 97 98 99

(Jan.1987=1)

Figure 4: Real E¤ective Exchange Rates

ADF test KP SS test REER t = 3:11(1) = 0:35(2) RER t = 2:57(3) = 1:42(4)

Table 1: Unit Root Tests

(1) reject the null hypothesis of unit root at 5% and 10%.

(2) Not able to reject the null hypothesis of stationarity at signi…cance levels 1% and 5%.

(3) Reject the null hypothesis of unit root at 10%.

(4) Reject the null hypothesis of stationarity at 10%, 5%, 1%.

model on RER hypothesis test statistic

a. t= 0+ t 1+ 2 t + "t = 0 ta= 3:01

= ₂= 0 F_a1= 1:47

0= = 2= 0 Fa2= 3:58

b. _t= ₀+ _{t 1}+ "_t = 0 t_b= 2:58( )

= 2= 0 Fb= 3:95

c. _t= _{t 1}+ "_t = 0 t_c= 1:49

Table 2: Unit Root Test on RER (*) signi…cant at 10% signi…cance level.

The subscript in the test statistics refers to the model a, b, or c.

Model a. The test of a unit root, ta, cannot be rejected at 10% signi…cance level. The test of joint hypotheses of no trend and a unit root cannot be rejected (Fa1). The joint hypotheses of no trend, no drift term, and a unit root cannot be rejected (Fa2).

Model b. The test of a unit root, tb, is rejected at 10% signi…cance level.

The joint hypotheses of a unit root and no drift term cannot be rejected.

Model c. The test of a unit root, t_c, cannot be rejected at 10% signi…cance level.

Test on the residuals: In all the models, the autocorrelations were small. The Ljung-Box Q statistics were not signi…cant at conventional levels: Q(5)=2.88, Q(10)=7.5, Q(20)=12.6 (model b). Similarly the Ljung-Box Q statistics of the squared residuals were not signi…cant at conventional levels Q(5)=1.65, Q(10)=6.3, Q(20)=10.9 (model b), which are indications of no ARCH/GARCH e¤ects.

t-value/one unit root t-value /two unit roots

f 2:29 9:8

p 2:10 14:4

Table 3: Test on the order of Integration

Dickey-Fuller critical values for the second column (constant and a trend):

1%: -4.0, 5%: -3.43, 10%: -3.14

Dickey-Fuller critical values for the third column (constant):

1%: -3.46, 5%: -2.87, 10%: -2.17

constant ₀ t-value one^{^}t critical values

06= 0 3:08) 3:06(10%)

0= 0 3:22 3:36(5%)

Table 4: Engle-Granger Test